Buzzard/Chords - Revision history

Lériendil: Lériendil moved page Chords of buzzard to Buzzard/Chords

2025-06-22T21:47:44Z

Lériendil moved page Chords of buzzard to Buzzard/Chords

← Older revision	Revision as of 21:47, 22 June 2025
(No difference)

FloraC: Cleanup

2025-01-26T09:44:02Z

Cleanup

← Older revision		Revision as of 09:44, 26 January 2025
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	Below are listed the [[15-odd-limit]] [[dyadic chord]]s of the [[buzzard]] temperament, subject to the condition that no interval smaller than [[12/11]], at 150 [[cent]]s, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[176/175]] are labeled [[~~Valinorsmic~~ chords\|valinorsmic]], by [[540/539]] [[~~Swetismic~~ chords\|swetismic]], by [[351/350]] [[~~Ratwolfsmic~~ chords\|ratwolfsmic]], by [[352/351]] [[~~Minthmic~~ chords\|minthmic]], by [[676/675]] [[~~Island~~ chords\|island]], by [[729/728]] [[~~Squbemic~~ chords\|squbemic]], by [[1001/1000]] [[~~Sinbadmic~~ chords\|sinbadmic]], by [[640/637]] [[~~Huntmic~~ chords\|huntmic]], by [[847/845]] [[~~Cuthbert~~ chords\|cuthbert]], by [[1188/1183]] [[~~Kestrel~~ chords\|kestrel]], and by [[2200/2197]] [[~~Petrmic~~ chords\|petrmic]]. [[Codimension]]-2 temperaments are labeled valinorsmic-ratwolfsmic, valinorsmic-huntmic, valinorsmic-island, valinorsmic-swetismic, swetismic-ratwolfsmic, swetismic-minthmic, swetismic-cuthbert, ratwolfsmic-island, minthmic-squbemic, ratwolfsmic-kestrel, minthmic-island, cuthbert-sinbadmic according to the two commas which define it. Finally, rank-3 temperaments are labeled [[guanyin]], [[draco]] or [[persephone]].		Below are listed the [[15-odd-limit]] [[dyadic chord]]s of the [[13-limit]] [[buzzard]] temperament, subject to the condition that no interval smaller than [[12/11]], at 150 [[cent]]s, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[176/175]] are labeled [[valinorsmic chords\|valinorsmic]], by [[540/539]] [[swetismic chords\|swetismic]], by [[351/350]] [[ratwolfsmic chords\|ratwolfsmic]], by [[352/351]] [[major minthmic chords\|minthmic]], by [[676/675]] [[island chords\|island]], by [[729/728]] [[squbemic chords\|squbemic]], by [[1001/1000]] [[sinbadmic chords\|sinbadmic]], by [[640/637]] [[huntmic chords\|huntmic]], by [[847/845]] [[cuthbert chords\|cuthbert]], by [[1188/1183]] [[kestrel chords\|kestrel]], and by [[2200/2197]] [[petrmic chords\|petrmic]]. [[Codimension]]-2 temperaments are labeled valinorsmic-ratwolfsmic, valinorsmic-huntmic, valinorsmic-island, valinorsmic-swetismic, swetismic-ratwolfsmic, swetismic-minthmic, swetismic-cuthbert, ratwolfsmic-island, minthmic-squbemic, ratwolfsmic-kestrel, minthmic-island, cuthbert-sinbadmic according to the two commas which define it. Finally, rank-3 temperaments are labeled [[guanyin]], [[draco]] or [[persephone]].

	Buzzard has [[mos scale]]s of size 5, 8, 13, 18, 28, 33, 38, 43, 48, 53, 58 and 111. The largest chords on these lists have complexity 42, and so would require the 43-note mos, but there are many chords of much lower complexity. The 8-note mos has a number of chords, the 13-note mos has a considerable store, and of course the 18-note mos many more.		Buzzard has [[mos scale]]s of size 5, 8, 13, 18, 28, 33, 38, 43, 48, 53, 58 and 111. The largest chords on these lists have complexity 42, and so would require the 43-note mos, but there are many chords of much lower complexity. The 8-note mos has a number of chords, the 13-note mos has a considerable store, and of course the 18-note mos many more.

	== Triads ==		== Triads ==

	The triads are listed in four ways.		The triads are listed in four ways.

	First, by number of generators, in the "transversal" column. This is a convenient way to see how many of these chords will appear in a given ~~MOS~~: For example, since it takes four generators to get to 1/~~1-26/15-3~~/2, you will have four of these chords in the 8-note ~~MOS~~ (8-4 = 4). Note that 8 generators means 9 notes: 9/8 ~~doesn't~~ appear in the 8-note ~~MOS~~.		First, by number of generators, in the "transversal" column. This is a convenient way to see how many of these chords will appear in a given mos: For example, since it takes four generators to get to 1–26/15–3/2, you will have four of these chords in the 8-note mos ({{nowrap\| 8 - 4 {{=}} 4 }}). Note that 8 generators means 9 notes: 9/8 does not appear in the 8-note mos.

	However, the notes may not appear in size order; 26/15 is 952 cents and 3/2 is 702 cents, so the chord would normally be written 1/~~1-3/2-26~~/15 -- which leads us to the second way chords are listed.		However, the notes may not appear in size order; 26/15 is 952 cents and 3/2 is 702 cents, so the chord would normally be written 1–3/2–26/15 – which leads us to the second way chords are listed.

	Second, as generated, but in size order.		Second, as generated, but in size order.
Line 17:		Line 16:
	Fourth, rotated to use the third note as the root.		Fourth, rotated to use the third note as the root.

	You can think of the third and fourth ways as the "first and second inversions" of the second way, but unlike conventional music theory, there's no preference for any one of the inversions over the other. Chords are chords are chords, and we look at the inversions because it can help to know that 1/~~1-8/7-12~~/7, ~~1/1-3~~/~~2-7~~/4, and 1/~~1-7/6-4~~/3 are all inversions or rotations of the same chord.		You can think of the third and fourth ways as the "first and second inversions" of the second way, but unlike conventional music theory, there is no preference for any one of the inversions over the other. Chords are chords are chords, and we look at the inversions because it can help to know that 1–8/7–12/7, 1–3/2–7/4, and 1–7/6–4/3 are all inversions or rotations of the same chord.

	Note that the values for these notes might have been attained by applying one of the commas noted in the introductory section.		Note that the values for these notes might have been attained by applying one of the commas noted in the introductory section.
Line 27:		Line 26:
	! Transversal		! Transversal
	! Type		! Type
	! Size ~~Order~~		! Size order
	! First ~~Rotation~~		! First rotation
	! Second ~~Rotation~~		! Second rotation
	\|-		\|-
	\| 1		\| 1
Line 921:		Line 920:

	== Tetrads ==		== Tetrads ==

	{\| class="wikitable center-1"		{\| class="wikitable center-1"
	\|-		\|-
Line 928:		Line 926:
	! Transversal		! Transversal
	! Type		! Type
	! Size ~~Order~~		! Size order
	! First ~~Rotation~~		! First rotation
	! Second ~~Rotation~~		! Second rotation
	! Third ~~Rotation~~		! Third rotation
	\|-		\|-
	\| 1		\| 1

FloraC: Recategorize

2023-08-19T16:11:03Z

Recategorize

← Older revision		Revision as of 16:11, 19 August 2023
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	[[Category:Dyadic chords]]		[[Category:Dyadic chords]]
	[[Category:Buzzard]]		[[Category:Buzzard]]
	[[Category:~~15-odd-limit~~]]		[[Category:Triads]]
			[[Category:Tetrads]]
			[[Category:Pentads]]
			[[Category:Hexads]]

FloraC: Cleanup (2/2)

2023-08-19T16:04:57Z

Cleanup (2/2)

Show changes

FloraC: Cleanup (1/2)

2023-08-19T15:58:39Z

Cleanup (1/2)

← Older revision		Revision as of 15:58, 19 August 2023
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	Below are listed the 15-limit [[~~Dyadic_chord\|~~dyadic ~~chords~~]] of [[~~Hemifamity_temperaments~~#Buzzard-13-limit\|buzzard temperament]], subject to the condition that no interval smaller than [~~[12/11\|~~12/11]], at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 176/175 are labeled valinorsmic, by 540/539 swetismic, by 351/350 ratwolfsmic, by 352/351 minthmic, by 676/675 island, by 729/728 squbemic, by 1001/1000 sinbadmic, by 640/637 huntmic, by 847/845 cuthbert, by 1188/1183 kestrel, and by 2200/2197 petrmic. [[~~Rank_and_codimension\|~~Codimension]] ~~two~~ temperaments are labeled valinorsmic-ratwolfsmic, valinorsmic-huntmic, valinorsmic-island, valinorsmic-swetismic, swetismic-ratwolfsmic, swetismic-minthmic, swetismic-cuthbert, ratwolfsmic-island, minthmic-squbemic, ratwolfsmic-kestrel, minthmic-island, cuthbert-sinbadmic according to two commas which define it. Finally, rank ~~three~~ temperaments are labeled [[~~Orwellismic_family#Guanyin-13-limit\|~~guanyin]], [[~~Cataharry_family#Draco-13-limit\|~~draco]] or [[~~Swetismic_temperaments#Persephone-13-limit\|~~persephone]].		Below are listed the 15-odd-limit [[dyadic chord]]s of the [[Hemifamity temperaments #Buzzard-13-limit\|buzzard temperament]], subject to the condition that no interval smaller than [12/11]], at 150 cents, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[176/175]] are labeled [[Valinorsmic chords\|valinorsmic]], by [[540/539]] [[Swetismic chords\|swetismic]], by [[351/350]] [[Ratwolfsmic chords\|ratwolfsmic]], by [[352/351]] [[Minthmic chords\|minthmic]], by [[676/675]] [[Island chords\|island]], by [[729/728]] [[Squbemic chords\|squbemic]], by [[1001/1000]] [[Sinbadmic chords\|sinbadmic]], by [[640/637]] [[Huntmic chords\|huntmic]], by [[847/845]] [[Cuthbert chords\|cuthbert]], by [[1188/1183]] [[Kestrel chords\|kestrel]], and by [[2200/2197]] [[Petrmic chords\|petrmic]]. [[Codimension]]-2 temperaments are labeled valinorsmic-ratwolfsmic, valinorsmic-huntmic, valinorsmic-island, valinorsmic-swetismic, swetismic-ratwolfsmic, swetismic-minthmic, swetismic-cuthbert, ratwolfsmic-island, minthmic-squbemic, ratwolfsmic-kestrel, minthmic-island, cuthbert-sinbadmic according to the two commas which define it. Finally, rank-3 temperaments are labeled [[guanyin]], [[draco]] or [[persephone]].

	Buzzard has ~~MOS~~ of size 5, 8, 13, 18, 28, 33, 38, 43, 48, 53, 58 and 111. The largest chords on these lists have complexity 42, and so would require the 43 note ~~MOS~~, but there are many chords of much lower complexity. The 8-note ~~MOS~~ has a number of chords, the 13-note ~~MOS~~ has a considerable store, and of course the 18-note ~~MOS~~ many more.		Buzzard has [[mos scale]]s of size 5, 8, 13, 18, 28, 33, 38, 43, 48, 53, 58 and 111. The largest chords on these lists have complexity 42, and so would require the 43-note mos, but there are many chords of much lower complexity. The 8-note mos has a number of chords, the 13-note mos has a considerable store, and of course the 18-note mos many more.

	=Triads=		== Triads ==

	The triads are listed in four ways.		The triads are listed in four ways.
Line 920:		Line 920:
	\|}		\|}

	=Tetrads=		== Tetrads ==

	{\| class="wikitable"		{\| class="wikitable"
Line 2,887:		Line 2,887:
	\|}		\|}

	=Pentads=		== Pentads ==

	{\| class="wikitable"		{\| class="wikitable"
Line 3,582:		Line 3,582:
	\|}		\|}

	=Hexads=		== Hexads ==

	{\| class="wikitable"		{\| class="wikitable"
Line 3,671:		Line 3,671:
	\| \| utonal		\| \| utonal
	\|}		\|}

	[[Category:Lists of chords]]		[[Category:Lists of chords]]
	[[Category:Dyadic chords]]		[[Category:Dyadic chords]]
	[[Category:Buzzard]]		[[Category:Buzzard]]
	[[Category:15-odd-limit]]		[[Category:15-odd-limit]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-25T10:58:32Z

Categorised this uncategorised page

← Older revision		Revision as of 10:58, 25 April 2023
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	\| \| utonal		\| \| utonal
	\|}		\|}
			[[Category:Lists of chords]]
			[[Category:Dyadic chords]]
			[[Category:Buzzard]]
			[[Category:15-odd-limit]]

Jdfreivald: /* Tetrads */ Added all of the rotations of the tetrads

2020-06-12T01:40:29Z

Tetrads: Added all of the rotations of the tetrads

Show changes

Jdfreivald: /* Triads */

2020-06-04T15:01:48Z

Triads

← Older revision		Revision as of 15:01, 4 June 2020
Line 7:		Line 7:
	The triads are listed in four ways.		The triads are listed in four ways.

	First, by number of generators, in the "transversal" column. This is a convenient way to see how many of these chords will appear in a given MOS: For example, since it takes four generators to get to 1/1-26/15-3/2, you will have four of these chords in the 8-note MOS. However, the notes may not appear in size order; 26/15 is 952 cents and 3/2 is 702 cents, so the chord would normally be written 1/1-3/2-26/15 -- which leads us to the second way chords are listed.		First, by number of generators, in the "transversal" column. This is a convenient way to see how many of these chords will appear in a given MOS: For example, since it takes four generators to get to 1/1-26/15-3/2, you will have four of these chords in the 8-note MOS (8-4 = 4). Note that 8 generators means 9 notes: 9/8 doesn't appear in the 8-note MOS.

			However, the notes may not appear in size order; 26/15 is 952 cents and 3/2 is 702 cents, so the chord would normally be written 1/1-3/2-26/15 -- which leads us to the second way chords are listed.

	Second, as generated, but in size order.		Second, as generated, but in size order.

Jdfreivald: /* Triads */ Fixed a typo.

2020-06-04T14:20:17Z

Triads: Fixed a typo.

← Older revision		Revision as of 14:20, 4 June 2020
Line 17:		Line 17:
	You can think of the third and fourth ways as the "first and second inversions" of the second way, but unlike conventional music theory, there's no preference for any one of the inversions over the other. Chords are chords are chords, and we look at the inversions because it can help to know that 1/1-8/7-12/7, 1/1-3/2-7/4, and 1/1-7/6-4/3 are all inversions or rotations of the same chord.		You can think of the third and fourth ways as the "first and second inversions" of the second way, but unlike conventional music theory, there's no preference for any one of the inversions over the other. Chords are chords are chords, and we look at the inversions because it can help to know that 1/1-8/7-12/7, 1/1-3/2-7/4, and 1/1-7/6-4/3 are all inversions or rotations of the same chord.

	Note that the values for these notes might have been attained by applying the ~~comma~~ noted in the introductory ~~second~~.		Note that the values for these notes might have been attained by applying one of the commas noted in the introductory section.

	{\| class="wikitable"		{\| class="wikitable"

Jdfreivald: Added rotations of the triads.

2020-06-04T14:18:48Z

Added rotations of the triads.

Show changes